They are looking into when he first knew that the carmaker was rigging diesel emissions tests.
It is the second investigation into Winterkorn's role in the scandal.
The former CEO is already being investigated over possible market manipulation.
VW's acknowledgement in September 2015 that it had used software to reduce emissions levels when cars were being tested in the United States wiped billions of euros from its market value, forced Winterkorn's resignation and led to investigations and lawsuits around the world.
VW has said its executive board did not learn of the software violations until late August 2015 and formally reported the cheating to U.S. authorities in early September that year.
Appearing before German politicians last week Winterkorn refused to say when he first learned about systematic exhaust emissions cheating but said it was no earlier than VW has officially admitted.
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